The closest thing to fix this issue was new service /storage/.config/system.d/kodi-reboot.service (shutdown.sh always gets reboot parameter):
Code
[Unit]
Description=Kodi reboot script
After=network.target
[Service]
Type=oneshot
Environment=HOME=/storage
ExecStart=/bin/true
ExecStop=-/bin/sh -c ". /etc/profile; exec /bin/sh /storage/.config/shutdown.sh reboot"
RemainAfterExit=yes
[Install]
WantedBy=kodi.target
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But for some reason it didn't work 100% reliably.